The Data Vortex: From Interbellum Polish Mathematics to a Novel - PDF document

The Data Vortex: From Interbellum Polish Mathematics to a Novel Topology for Connecting Cores 1 Coke S. Reed 1 , Reed E. Devany 1 , Michael R. Ives 2 , Santiago I. Betelu 1,3 1 Data Vortex Technologies, 2 Plexus Corp, 3 University of North Texas Slide 1 (Title Slide) : Good afternoon. Or, if you’re here in the States, good morning. My name is Reed Devany and I am one of the authors of “The Data Vortex: From Interbellum Polish Mathematics to a Novel Topology for Connecting Cores.” My co-authors are here today and will be available at the end of this presentation to answer any of your questions. Slide 2 : Today’s talk will be divided into five categories: the Polish roots of the Data Vortex, a description of the Data Vortex topology, the nature and performance of legacy Data Vortex validation systems, using the Data Vortex for direct core-to-core communication, and novel application areas that can address today’s pressing problems. Data Vortex Technologies holds the unique distinction of being a multi-generation family computing company. My grandfather, Dr. Coke Reed, pictured here of the left, is the inventor of the Data Vortex and Chairman, my mother, Carolyn Devany, is the CEO, and I, Reed Devany, am the Communications Director and an intellectual property author and coordinator. Here we are at SC16 in Salt Lake City, receiving an HPCwire award from Tom Tabor for best collaboration between industry and government. 1 Note: This paper was presented at Supercomputing Frontiers Europe (SCFE) 2020 on March 25, 2020. The event was remotely held as a teleconference due to the 2020 COVID-19 outbreak. Thus, while SCFE was hosted in Warsaw, Poland, the talk itself was delivered in Austin, Texas. The paper is broken up to match the presentation. If you would like a copy of the slides, pleas reach out to reed@datavortex.com. 1 | P a g e

My grandfather’s story and the story of the Data Vortex have deep roots in the Polish mathematical tradition, so I am honored to present this paper to our hosts at the University of Warsaw. Slide 3 : During the Interbellum period between the World Wars, Lwow, Poland (present-day Lviv, Ukraine) was a major seat of topological mathematics. The University of Lwow’s mathematics faculty, including John von Neumann, Stefan Banach, Stanislaw Ulam, and Leopold Infeld, met at the Scottish Café to discuss their theorems and problems. Some mathematicians speculate it was the most productive café in the history of Europe. Problems that an individual could not solve were written down in the “Scottish Book” and left as a challenge for their colleagues, oftentimes with prizes offered. Many of these mathematicians left Poland for the United States prior to the Second World War and joined the Manhattan project, primarily in Los Alamos, New Mexico. The Scottish Book was left behind and buried under Lwow University’s football pitch for safekeeping. Following the successful development of the atomic bomb and the end of the War, many of the Poles accepted positions with American universities, bringing with them their unique traditions and research areas, including topological dynamics. Banach’s wife, who had remained in Poland with her husband, retrieved the Scottish Book and sent it to Los Alamos. Slide 4 : “Problem 110” of the Scottish Book is the forefather of the Data Vortex. On October 1 st , 1935, Ulam posited a problem regarding the flow of particles in a dynamical system: 2 | P a g e

LET M BE A GIVEN MANIFOLD. Does there exist a numerical constant K such that every continuous mapping ƒ of the manifold M into part of itself which satisfies the shown condition: | ƒ n x – x | < K for n = 1,2, . . . [ƒ n denotes the n th iteration of the image ƒ(x) ] posses a fixed point: ƒ(x 0 ) = x 0 ? This problem, which von Neuman attempted in 1937, remained unsolved well into the 1970s. Coke Reed and Polish Mathematician Krystyna Kuperberg (both of Auburn University) discovered the solution and provided a counter-example, in which the manifold is Euclidian Three-Space. The associated prize? A bottle of wine. Upon sending Ulam the solution, Reed and Kuperberg received a three-word telegram, “Red or white”. Slide 5 : The solution, shown here, was published in Fundementae Mathematica as, “A rest point free dynamical system on R 3 with uniformly bounded trajectories” in 1981. As you can see in Figure One, the form of a vortex has begun to take shape. Slide 6 : Coke Reed spent the closing decades of the 20 th century working with the United States intelligence community and had accounts on Seymour Cray’s first machines. During this time, he began to consider how the mathematical solution to “Problem #110” could be modified to describe and reinvent data movement within a system. As many of those present can attest, great ideas rarely come in the laboratory or at one’s desk. One afternoon in the early ‘90s, Reed went on a walk in Rocky Mountain National Park with his beloved Labrador, Chloe. While staring into the mountains, the solution to his quandary appeared, and thus the “Data Vortex” was born. 3 | P a g e

What began as a walk in the woods has since grown into a vibrant company, made up of an intelligent team and exciting partnerships. Slide 7 : In 1995, Reed patented “A Multi-Level, Minimum-Logic Network”. The ring structure of the Problem 110 solution, which carried particles, inspired this structure, which carries information, a dynamic system of three-dimension Euclidean space. Slide 8 : The Data Vortex topology allows for small packet data flow that is high radix, self-routing, congestion free and is enabled by fine-grained parallelism. This is important for networks that need high bandwidth yet low latency and, importantly, are linearly scalable. Slide 9 : The Data Vortex topology can replace the crossbar within all points of the IT ecosystem. Crossbars like long packets and with long packets come a series of problems. Time is spent using an algebraic algorithm to set the switch, which is “hidden” by data transmission. Since low radix switches require many hops, high radix cross bar switches are chosen to reduce the number of hops. Higher radix crossbars require more time to set, resulting in longer packets. Slide 10 : The Data Vortex does not have this setting problem, thus the packets can remain short. It consists of a collection of richly connected rings. The rings and the connection between the rings are built using parallel data busses. In a Radix R switch with R =2 N , the rings are arranged at N +1 levels. A packet on the entry level, level N , the outermost level, can travel to any of the output ports. When 4 | P a g e

a packet travels from level N to level ( N -1), the most significant bit of the binary address of the output is fixed so that a packet on level N -1 can reach only half of the output ports; a packet on level N -2 can reach only one fourth of the output ports and so forth. This process continues so that when a packet reaches level 0, the target output is determined. To overcome the problem of algebraic setting (causing the use of long packets) the network must be self-routing. A possible solution is for the network to be a dynamical system DV that is discrete in both time T and space S . DV is a function that is defined on the whole space S. The state of the whole space S at time t must be known in order to know the state of the whole space S at time t+1. By definition of a dynamical system: if x and y are in T and p is a point of S then DV (0,p) = p and DV [x+y,p] = DV [x, DV (y,p)] Slide 11: The Data Vortex Network is thus a dynamical system that carries data. There is no switch setting for data movement management as in a crossbar, which is set by an algebraic algorithm. Data can be dropped into the flow of the system and transfer can be variable in size and can originate from a variety of inputs. A packet’s trajectory through the network is dependent on the packet header and the location and movements of the other packets in the switch. Slide 12: What started as a solution to an unsolved problem has become central element of our technology, the “Data Vortex switch.” On the right is Kuperberg’s work on the Siefert conjecture, another example of derivative work from Problem #110. More than two dozen global patents on the Data Vortex switch have been filed and published over the past twenty years, each of them playing an important role in solidifying the portfolio of this revolutionary technology. This intellectual 5 | P a g e